Upgrade radio or add Aux or BT

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Someone will be along shortly to offer advice.

You should be able to swap in an aftermarket radio with minimal issues. Do some research on websites like Crutchfield.com to get an idea of what you're need and what will fit. Metra makes a good wiring adapter for use between the new radio and the OEM wiring harness.
I honestly don't know if radios now even have the Aux option, I've been running bluetooth for a while.

I speak with owenr of the car and he said, AUX input its here but dont work, when he click to AUX button its start play radio, i hope its something what its possible to fix/repair

Does he have an aux cord plugged in when he selects it?
As for repair, it would be easier to either install an aftermarket radio or try to find another OEM unit.
Likely the 3.5mm jack is worn out and the "override tab" inside the jack is not making a connection with the plug.

With the technology floating around these days, I can't believe a good radio shop couldn't provide what you need. While, my Mustang is a 2008, I was able to have installed upgraded radio, CD, Navigation and back up camera in my car.